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From closed to open one-dimensional Anderson model: transport versus spectral statistics
S Sorathia1, F M Izrailev, V G Zelevinsky
1Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla, Puebla 72570, Mexico.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
We found a linear relationship between a quantum chaos parameter (β) and the normalized localization length in finite quantum systems. This simplifies describing transport properties in chaotic and complex systems.
Area of Science:
- Quantum physics
- Condensed matter physics
- Chaos theory
Background:
- Understanding transport properties in disordered quantum systems is crucial.
- The Anderson model describes electron localization in disordered materials.
- Characterizing chaos and complexity in quantum systems requires robust parameters.
Purpose of the Study:
- To establish a universal parameter for describing transport properties in finite quantum systems.
- To investigate the relationship between chaos and localization in the Anderson model.
- To explore the interplay between internal chaos and system openness.
Main Methods:
- Utilizing a phenomenological expression for level spacing distribution with a single parameter (β).
- Analyzing the one-dimensional Anderson model of finite size.
- Calculating the normalized localization length and its relation to β.
Main Results:
- A strictly linear relationship was found between parameter β and normalized localization length across all regimes.
- Transport properties of the finite Anderson model can be universally described by β and coupling strength.
- An unusual interplay between internal chaos (β) and system openness was observed for nonperfect coupling.
Conclusions:
- Parameter β provides a unified description for transport properties in finite quantum systems.
- The findings offer a new perspective on chaos-driven localization and transport.
- Experimental verification is possible in single-mode waveguides with controlled disorder.
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